This thesis describes extensions of the goal-oriented approach for
a posteriori error estimation and control of numerical
approximation to a class of highly-nonlinear problems in computational solid
mechanics. A new updated Lagrangian
formulation and an Arbitrary Lagrangian Eulerian (ALE) formulation of
the dynamic, large-deformation response of structures composed of
strain-rate-sensitive
elastomers and elastoplastic materials is developed. To apply the theory of
goal-oriented error estimation, a backward-in-time dual formulation of these
problems is derived, and residual error estimators for meaningful
quantities of interest are established. The target problem class is
that of axisymmetric
deformations of layered elastomer-reinforced shells-of-revolution immersed
in water and subjected to shock loading due to the ignition of explosive
materials in the water in the proximity of the shell. Extensive numerical
results on solutions of representative problems are given. It is shown
that extensions of the theory of goal-oriented error estimation can
be developed and applied effectively to a class of highly-nonlinear,
multi-physics problems in solid and structural mechanics.